This blog will follow my trials and tribulations playing live mid stakes Texas Hold'Em throughout California.

Friday, August 13, 2010

Variance Simulator

I don't know if I've ever put this up on my blog, so here is a really fun variance simulator for limit hold 'em (or any other game that you can define in terms of an expected win rate and standard deviation per some unit). The default units are "per 100 hands", but you can easily trick it into "per hour" if you put in the right data. For example, if you wanted to simulate a full time year in the life of me, a 20/40 player, make the following entries:

Winrate: 40

SD: 440 (this is an estimate but it's within 10%)

Hands: 200000 (2000*100 and we're trying to simulate 2000 hours)

# of Players: 100

The graph you get is the result of running an experiment where 100 players with the above true win rates and standard deviations play for 2000 hours. The results are pretty mind boggling if you're not ready for it. If you couple in playing multiple stake levels they get even worse; imagine what it could look like if each player took 400 of his hours off this graph and added in 400 hours at double the stakes, in a tougher and more aggressive game, where his win rate went up by only 60-80% (or not at all), but his standard deviation increased by say 125%. That's basically what I did in the second half of 2009, which turned out to be a complete disaster. I think I mentioned on here that at one point I had 200 hour stretch where I won exactly 1 big bet per hour but broke even, due to playing everywhere from a little 6/12 all the way up to 40/80.

I used to run these simulations using a true win rate of $50/hour, and admittedly they look a lot better when you do that. The constant tidal wave of positive expectation keeps the downswings and break even stretches much shorter; you're just absolutely crushing the game. But as you reduce that number towards the "accepted" maximum win rate, you start getting a lot of the artifacts you see here, with guys winning less than $20,000 for an entire year, or being under water for 1500 hours. Enjoy the toy.

5 comments:

I'll bite. Why is the answer not no? It seems pretty intuitive that if you dropped the win rate to zero that exactly 50% (in the long run) should end up in the black. Expected value changes are always constant shifts on graphs so to me it seems like exactly 50% of the walks should top $80K.